64.7.13 problem 13

Internal problem ID [13387]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page 67
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 05:36:45 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (-2\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.293 (sec). Leaf size: 20

dsolve([(2*x+3*y(x)+1)+(4*x+6*y(x)+1)*diff(y(x),x)=0,y(-2) = 2],y(x), singsol=all)
 

\[ y = \frac {1}{3}-\frac {2 x}{3}+\frac {\operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {x}{3}+\frac {4}{3}}}{3}\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.934 (sec). Leaf size: 30

DSolve[{(2*x+3*y[x]+1)+(4*x+6*y[x]+1)*D[y[x],x]==0,{y[-2]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} \left (3 W\left (\frac {2}{3} e^{\frac {x+4}{3}}\right )-4 x+2\right ) \]